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2 cards from this section. Quick, good the night before a test.
What does the binomial distribution model?
Consider what outcomes are being counted.
Explain what is meant by 'choosing k successes.'
Think about how many sequences can be formed.
What is (n choose k)?
Think of it as counting ways to pick items.
The binomial distribution can only be used if trials are independent.
Consider the definition of independent trials.
A factory produces 100 lightbulbs, and there's a 5% chance any bulb is defective. What’s the probability that exactly 3 bulbs are defective?
Break the calculation into the binomial coefficient and separate terms for success and failure.
In a game, you roll a die 30 times and win by rolling a 4 (p = 1/6). What’s the probability of rolling exactly 5 fours?
Calculate the combinations and the probabilities separately to build the answer.
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